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Mirrors > Home > ILE Home > Th. List > eluz | Unicode version |
Description: Membership in an upper set of integers. (Contributed by NM, 2-Oct-2005.) |
Ref | Expression |
---|---|
eluz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluz1 9330 | . 2 | |
2 | 1 | baibd 908 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 1480 class class class wbr 3929 cfv 5123 cle 7801 cz 9054 cuz 9326 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-cnex 7711 ax-resscn 7712 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fv 5131 df-ov 5777 df-neg 7936 df-z 9055 df-uz 9327 |
This theorem is referenced by: uzneg 9344 uztric 9347 uzm1 9356 eluzdc 9404 fzn 9822 fzsplit2 9830 fznn 9869 uzsplit 9872 elfz2nn0 9892 fzouzsplit 9956 exfzdc 10017 fzfig 10203 faclbnd 10487 seq3coll 10585 cvg1nlemcau 10756 cvg1nlemres 10757 summodclem2a 11150 fsum0diaglem 11209 mertenslemi1 11304 prodmodclem2a 11345 zsupcllemstep 11638 zsupcl 11640 infssuzex 11642 uzdcinzz 13005 |
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